cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A356662 a(n) = n! * Sum_{d|n} 1/(d!)^(n/d - 1).

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%I A356662 #13 Aug 21 2022 09:26:51
%S A356662 1,4,12,60,240,1740,10080,87360,735840,7514640,79833600,976686480,
%T A356662 12454041600,175736040480,2616448554720,42011071502400,
%U A356662 711374856192000,12830610027755520,243290200817664000,4870565189425615680,102182981410948838400,2249099140674523737600
%N A356662 a(n) = n! * Sum_{d|n} 1/(d!)^(n/d - 1).
%F A356662 a(p) = 2 * p! for prime p.
%F A356662 E.g.f.: Sum_{k>=1} x^k/(1 - x^k/k!).
%t A356662 a[n_] := n! * DivisorSum[n, 1/(#!)^(n/# - 1) &]; Array[a, 22] (* _Amiram Eldar_, Aug 21 2022 *)
%o A356662 (PARI) a(n) = n!*sumdiv(n, d, 1/d!^(n/d-1));
%o A356662 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/(1-x^k/k!))))
%Y A356662 Cf. A061095, A098558, A356543, A356661.
%K A356662 nonn
%O A356662 1,2
%A A356662 _Seiichi Manyama_, Aug 21 2022